All things are Related
Water leaking onto a floor forms a circular pool. The radius of the pool increases at a rate of 5 in/min. How fast is the area of the pool increasing when the radius is 4 in?
40pi in2/min
A rancher wants to construct two identical rectangular corrals using 200 m of fencing. The rancher decides to build them adjacent to each other, so they share fencing on one side. What dimensions should the rancher use to construct each corral so that together, they will enclose the largest possible area?
25m by (100/3)m
In what year was the first iPhone released?
2007
critical points
Find the intervals where the function is concave up and down:
y=x2-2x-3
CC-up (inf, inf)
A hypothetical square grows so that the length of its sides are increasing at a rate of 6m/min. How fast is the area of the square increasing when the sides are 2m each?
24 m2/min
A cryptography expert is deciphering a computer code. To do this, the expert needs to minimize the product of a positive rational number and a negative rational number, given that the positive number is exactly 6 greater than the negative number. What final product is the expert looking for?
-9
Where were the last two winter olympics held (100 pts each)
Beijing 2022
PyeongChang 2018
Points where the second derivative is either equal to zero or does not exist are called
Inflection points
find the intervals of concavity for the following function:
y=-x3+3x2-5
cc-up: (-inf, 1) cc-down: (1, inf)
A hypothetical square grows so that the length of its diagonals are increasing at a rate of 7 yd/min. How fast is the area of the square increasing when the diagonals are 4 yd each?
28 yd2/min
Engineers are designing a box-shaped aquarium with a square bottom and an open top. The aquarium must hold 256 m³ of water. What dimensions should they use to create an acceptable aquarium with the least amount of glass?
8m by 8m by 4m
What is the most abundant gas in the atmosphere?
Nitrogen
Find: increasing/decreasing, concavity, critical points, inflection points, intercepts, asymptotes and sketch the function.
y=x2-x-2
Dec: (-inf, 1/2), Inc: (1/2, inf), min at (1/2,-9/4)
Concave up: (-inf, inf)
x-intercepts: (-1,0) and (2,0), y-int: (0,-2)
First team to get it wins.
Find the intervals of concavity:
y=-x2+34x+pi
cc-down (inf, inf)
A 25 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 3 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 24 ft from the wall?
7/8 ft/sec
A graphic designer is asked to create a movie poster with a 98 cm² photo surrounded by a 4 cm border at the top and bottom and a 2 cm border on each side. What overall dimensions for the poster should the designer choose to use the least amount of paper?
11cm by 22cm
Who wrote the novel 1984?
George Orwell
y=2/(x-2)
Dec: (-inf, 2) U (2, inf), No max/min
concave down: (-inf, 2), cc-up: (2,inf)
Asymptotes: x=2 and y=0
First team to get it wins, find the intervals of concavity.
y=1/(x+7)
cc-down: (inf, -7) cc-up: (-7, inf)
Complete the list for 100 points each:
Triangle, quadrilateral, pentagon, _____, _____, _____, _____, _____,
Hexagon, heptagon, octagon, nonagon, decagon